I'm considering a Fighter 1/Monk 1/Rogue 18 for a character. Our DM has a few house rules that I want to take full advantage of by combining Great Weapon Fighting's rerolls with Sneak Attacks.

Specifically, the rulings involved are:

Monk weapons have the finesse property when wielded by a monk.

GWF's reroll applies to extra damage dice, not just weapon dice.

Multi-classing is permitted, obviously.

Flanking rules from the DMG are being used.

Now, a monk/rogue/fighter can combine these like so:

Use a versatile weapon two-handed (e.g., quarterstaff), to activate GWF

Flank an enemy to enable Sneak Attacks

Attack using +Dex, gaining bonus damage dice from Sneak Attack, which can all benefit from GWF's benefit of rerolling 1s and 2s on damage dice

The question is, how does this stack up against other known good builds?

The two benchmarks I have in mind to measure this against are the Great Weapon Master + Polearm Master strategy, and the Sharpshooter + Crossbow Expert strategy. I know these are strong, especially if one has CA and (for the Polearm one) has good use of action economy to get more DPR.

And if I got a hold of a Sun Blade (DMG p. 205), with its inherent finesse property, I could do without the 1-level dip into Monk. Would that significantly change how the build compares to the benchmarks?

1 Answer
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Let's work out some of the math here; the details of your build and your DM are going to influence how these numbers work out. Some assumptions I am making based on what you have stated.

Assumptions

You said DM is letting you use flanking rules so I am assuming you are getting advantage on each attack so I am going to state that you are getting advantage on your rolls 75% of the time due to other skills and tactics you could be doing.

I am assuming that your attack stat at this point is a 20 in any of the builds. I am ignoring barbarians right now who can get more then a 20 in a stat also I am ignoring belts or other items that can raise your stat above a 20.

Finally we are going to ignore the Sun Blade because getting a hold of a specific magic item should not be a requirement for a build.

This also assumes that your DM lets you roll your X number of attacks and decide to apply the sneak attack to the critical attack. The once per term requirement is very vague on this and should be clarified.

The Math

My first thought is that the thief build is going to be really top heavy; you are trying to get as many dice rolls as possible because you want that natural 20 critical to double the number of dice you are rolling for damage. I did a little look at monsters vs stats and I am trying to figure out a good threshold for when a die roll will hit and I feel like 13 on the die should hit based on average AC of monsters at that level. So 13 for die roll, 2 for weapon bonus, 6 for proficiency and 5 for stat. Now one could argue these numbers one way or another but I am going to be using them as the base because I need something to compare apples to apples.

So 13 + 2 + 6 + 5 = 26 for target AC to hit or 35% chance to hit and a 5% chance to crit. I used http://andrewgelman.com/2014/07/12/dnd-5e-advantage-disadvantage-probability/ as a reference for determining advantage so that translates to a 63.9% chance to hit and a 9.8% to critical. That makes it so 54.1% of the time you are going to do normal damage and 9.8% time you are going to do double damage. I basically am saying 2/3 of the time you are going to hit with your attack, really anything that gives you 2 attacks is going to let you get a sneak attack in during that round so long as you are within 5 feet of your target. This is also a pretty high number, some could argue that 10 or above would be a more realistic number then you are talking almost an 80% chance to hit with advantage.

Since you decided to dip into fighter instead of go 20 rogue you don't get Stroke of Luck but that would only be a factor depending on how much resting vs combat you would do. To ease math on calculating average damage I am assuming your weapon damage for rogue is a D6. If you are getting a D8 or better this just slightly makes your numbers better it just helps me to do my math faster.

Critical Hit - 18d6 + 2d6 + 5 + 2 = 77 Avg

Normal Hit - 9d6 + 1d6 + 5 + 2 = 42 Avg

GWF Critical Hit - 18d6 + 2d6 + 5 + 2 = 85 Avg

GWF Normal Hit - 9d6 + 1d6 + 5 + 2 = 46 Avg

The math was kind of surprising because of the limited reroll only on 1 or 2 and you could get a 1 after you rerolled a 2 but on average on 10d6 rolling a 1 or 2 and getting 4 extra damage on average.

Polearm Master

After looking at the polearm master the numbers are basically the same for attack and damage except that you get another attack that you will get your critical damage against. Even though the base dice is a d4 that extra attack is what gets you the key advantage — do you want that extra damage from the reroll or the chance to attack again and be able to sneak attack? Frankly I'd rather take the 63.9% to do my sneak attack dice again then the extra 4 damage on average.

Crossbow Expert

This basically follows the same rules as Polearm master: the feat is letting you get an extra attack with the a crossbow and I still think it is better then Polearm master because being able to attack at range is crucial; however, that depends on your flavor and what you like to do. However where this starts to break down is flanking and how your GM rules on flanking with a crossbow. If your GM rules you can't with a range weapon then you are stuck with polearm.

Bottom Line

Bottom line your GM house rule about flanking is getting you the most bang for your buck here because you want to maximize that rule. The winner between all 3 is really hard to decide, and also depends on how your GM house rules critical hits and determining which one was a sneak attack. If you get to pick the extra attack is going to be always worth it. If you can't pick which attack to apply sneak attack damage to then they are really almost a wash because your extra critical chance vs the on average higher damage from your rolling is going to end up being almost a wash in the long term at high level.

\$\begingroup\$The whole point of the question was his ability to reroll 1s and 2s, which you haven't included in your damage calculations.\$\endgroup\$
– MinimanAug 14 '15 at 23:07

\$\begingroup\$I have if you see the lines with GWF, I have with sneak attack, with normal attacks, the statistical increase of damage is approx 1 over the long term with a small number of dice, for 10 dice the increase in damage expected is approx 4. That gives you the basis for a long term benefit. What really caused a skew in the numbers was critical sneak attacks which had 18d6 which made the numbers really top heavy it really only pays on crits and 8 damage is approx the amount you gain from the rerolls.\$\endgroup\$
– JamesAug 15 '15 at 13:37

\$\begingroup\$I don't think so the other people calculated at d6: +19% damage I had the numbers be closer to 17% because of the long term rerolls on damage, at least that is the numbers I ran through mathmatica. Still there isn't much different between 4 damage over 10 rolls vs 5 damage over 10 rolls.\$\endgroup\$
– JamesAug 15 '15 at 14:18

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\$\begingroup\$The point I was trying to make with this is average damage doesn't make this combination that effective unless you have a higher die weapon damage or a greatsword that has 2d6. For a thief what makes this decent is being able to crit on your sneak attack because you get that many more dice to factor in the reroll.\$\endgroup\$
– JamesAug 15 '15 at 14:20